Question

There are three urns containing 2 white and 3 black balls, 3 white and 2 black balls, and 4 white and 1 black balls, respectively. There is an equal probability of each urn being chosen. A ball is drawn at random from the chosen urn and it is found to be white. Find the probability that the ball drawn was from the second urn. Select the correct answer from above options

Answer 1

Given, we have 3 urns: Urn 1 = 2 white and 3 black balls Urn 2 = 3 white and 2 black balls Urn 3 = 4 white and 1 black balls Now, the probabilities of choosing either of the urns are P(U1) = P(U2) = P(U3) = 1/3 Let H be the event of drawing white ball from the chosen urn. So, P(H/U1) = 2/5, P(H/U2) = 3/5 and P(H/U3) = 4/5 By using Baye’s Theorem, we have Therefore, the required probability is 1/3.